We have an infinite sequence of random variables which are exchangeable. Could we say that each finite subsequence of this sequence is again exchangeable?
By definition, an infinite collection of random variables is said to be exchangeable if every finite subset of those variables is exchangeable. (See definition 1.11 in Schervich's book "Theory of statistics" (p.7).
A finite collection of finite random variables is said to be exchangeable if their distribution is invariant under permutations.